Direct tunneling vs. vibrational assisted transport. Until
this point (and beyond this subsection) we have taken \(v_{da}=0\) . We
now evaluate the contribution of different transport mechanisms by
adding a direct D-A tunneling term, \(v_{da}\ne 0\)  to our model
Hamiltonian. Electrons can now either cross the junction in a
coherent manner, or inelastically, by exciting/de-exciting the
vibrational mode. Fig. REF  demonstrates that when the
vibration assisted transport energy \(\kappa \)  is identical in
strength to the direct tunneling element \(v_{da}\) , the overall
current is enhanced by about a factor of two, compared to the case
when only vibrational-assisted processes are allowed. We also note
that the occupation of the vibrational mode is barely affected by the
opening of the new electron transmission route (deviations are
within the convergence error). While we compare IF data to Master
equation results when \(v_{da}=0\) , in the general case of a nonzero
D-A tunneling term perturbative methods are more involved, and
techniques similar to those developed for the AH model should be
used [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}.
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